Saturday, December 19, 2009

Big Numbers


Lately we have been hearing some very large numbers bandied about – so large, in fact, that I am not sure we understand just how large they really are. Some examples: Bill Gates’ net worth is $40 billion, the population of China is 1.17 billion people, the U.S. national debt is limited to $12.1 trillion, etc. How can one picture that much of anything?
Let’s imagine we have a machine which can take us back in time as far as we want to go. We can set it for any amount of time we choose, go back that far, and see where we land.
Suppose we start with one billion seconds. Will we open the door on last week, last month, five years ago – When? Close the door, set the dial, push the button, and when the shaking stops, open the door.
Welcome to April, 1977! Jimmy Carter became president in January, Star Wars will open next month, a gallon of gas will set you back 64 cents, and Elvis has about four months to live.
Suppose we set the dial for one billion minutes and try again. Will we meet George Washington, talk to Shakespeare or join the Crusades? Push the button…
And we are in 106 C.E. Trajan has just defeated the Dacians, and 10,000 of them have been sent to Rome to die as gladiators in the arena. Ignatius, the third bishop of Antioch has written a letter to the Christians in Smyrna, in which he used the term “Catholic Church” for the first time. The crucifixion occurred about 70 years ago, and Mohammed will be born in another 465 years. Let’s see what happened one billion hours ago. The button, please.
Welcome to 112,000 B.C.E.: the Pleistocene era. Flowering plants, insects, birds and mammals are not much different from those of today, although some, e.g. mammoths and mastodons will eventually become extinct. Neanderthals are the reigning humanoid species – modern homo sapiens is a small minority; a deficiency to be overcome in the next 50,000 years. Let’s try one more trip. Button again, please.
There is not much that we would recognize in the Mesoproterozoic era. Living organisms consist mostly of bacteria, although some cells with a nucleus, eukaryotes, are also showing up. Stable continents appeared some time prior to this, although 700 or 800 million  years from now the Australian and American continents will begin to drift away from the super-continent: Pangea. Let’s go home.
It is impossible to illustrate one trillion on a time scale, because a trillion years is 75 times as long as the universe has existed. We can get some idea of its magnitude by realizing that if scientists were to discover 155 planets with a population similar to earth’s, that would add up to one trillion people.
So when we begin to grasp some idea of the scope of the huge numbers kicked around in Washington, we have to agree with a comment attributed to the late Senator Everett Dirksen, " A billion here, a billion there, and pretty soon you're talking real money."

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